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Polysomnographic (sleep) signals are recorded from patients exhibiting symptoms of a suspected sleep disorder such as Obstructive Sleep Apnoea (OSA). These non-stationary signals are characterised by having both quantitative information in the frequency domain and rich, dynamic data in the time domain. The collected data is subsequently analysed by skilled visual evaluation to determine whether arousals are present, an approach which is both time-consuming and subjective. This paper presents a wavelet-based methodology which seeks to alleviate some of the problems of the above method by providing: (a) an automated mechanism by which the appropriate stage of sleep for disorder observation may be extracted from the composite electroencephalograph (EEG) data set and (b) an ensuing technique to assist in the diagnosis of full arousal by correlation of wavelet-extracted information from a number of specific patient data sources (e.g. pulse oximetry, electromyogram [EMG] etc.).

The advent of multiple electrode recording, dense arrays and mathematical techniques such as non-linear dynamics has invigorated brain electrical recording techniques. Taking advantage of the excellent temporal resolution of the EEG, this summary review details several innovations, concentrating on (1) the rapid changes in electrical activity and a consequent stable complex pattern; and (2) the utilization of engineering techniques that have been applied across scales ranging upward from quantum physics. The implications for brain localization and for communication science are developed.

Continuum simulations of cortical dynamics permit consistent simulations to be performed at different spatial scales, using scale-adjusted parameter values. Properties of the simulations described here accord with Freeman's experimental and theoretical findings on gamma synchrony, phase transition, phase cones, and null spikes. State equations include effects of retrograde action potential propagation into dendritic trees, and kinetics of AMPA, GABA, and NMDA receptors. Realistic field potentials and pulse rates, gamma resonance and oscillation, and 1/f² background activity are obtained. Zero-lag synchrony and traveling waves occur as complementary aspects of cortical transmission, and lead/lag relations between excitatory and inhibitory cell populations vary systematically around transition to autonomous gamma oscillation. Autonomous gamma is initiated by focal excitation of excitatory cells and suppressed by laterally spreading trans-cortical excitation. By implication, patches of cortex excited to gamma oscillation can mutually synchronize into larger fields, self-organized into sequences by mutual negative feedback relations, while the sequence of synchronous fields is regulated both by cortical/subcortical interactions and by traveling waves in the cortex — the latter observable as phase cones. At a critical level of cortical excitation, just before transition to autonomous gamma, patches of cortex exhibit selective sensitivity to action potential pulse trains modulated in the gamma band, while autonomous gamma releases pulse trains modulated in the same band, implying coupling of input and output modes. Transition between input and output modes may be heralded by phase slips and null spikes. Synaptic segregation by retrograde action potential propagation implies state-specific synaptic information storage.

Spanness of fuzzy graph is introduced. By spanness, a new vulnerability parameter, span integrity is defined in fuzzy graph. The span integrity values are found for path, cycle, complete fuzzy graph, complete bipartite fuzzy graphs. Path and cycle with node strength sequence are discussed. Brain network is modeled as a fuzzy graph and Span integrity is applied to the brain network. Span integrity of fuzzy brain network is calculated for before and after meditation models. The results are compared and the improvement in the stability of the brain network is shown.

A human brain is the most important organ which controls the functioning of the body including heartbeat and respiration. It is an extremely complex system. Electroencephalography (EEG) is the recording of electrical activity along the scalp produced by the firing of neurons within the brain. In clinical context EEG refers to the recording of the brain's spontaneous electrical activity over a short period of time, say 20-40 minutes, as recorded from multiple electrodes placed on the scalp. The main application of EEG is in the case of epilepsy, as epileptic activity can create clear abnormalities on a standard EEG study. A secondary clinical use of EEG is in coma, Alzheimer's disease, encephalopathies, and brain death. However in the recent years EEG is also being used to design the brain of a robot. Mathematical concepts specially methods for numerical solution of partial differential equations with boundary conditions, inverse problem methods and wavelet analysis have found prominent position in the study of EEG. The present paper is devoted to this theme and will highlight the role of wavelet methods. It will also include the results obtained in our research project.